Problem: Rewrite as a simplified fraction. ${1.\overline{51} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 151.5151...\\ 1x &= 1.5151...\end{align*}}$ Subtracting the two equations, we have: ${99x = 150}$ ${x = \dfrac{150}{99}} $ ${x = \dfrac{50}{33}} \text{or} {1 \dfrac{17}{33}}$